Time dependent gamma-ray production in the anisotropic IC $e^\pm$ pair cascade initiated by electrons in active galaxies

Abstract

New high energy emission features have been recently discovered by the Cherenkov telescopes from active galaxies e.g., a few minutes variability time scale of TeV emission from Mrk 501 and PKS 2155-304, sub-TeV $γ$-ray emission from GeV peaked blazar 3C 279, and TeV emission from two nearby active galaxies, M87 and Cen A, which jets are inclined at a relatively large angle to the line of sight. These results have put a new light on the high energy processes occurring in central parts of active galaxies stimulating more detailed studies of $γ$-ray emission models. Here we report the results of a detailed analysis concerning the most general version of the model for the $γ$-ray production by leptons injected in the jet which interact with the thermal radiation from an accretion disk (the so called {\it external inverse Compton model}). We investigate the $γ$-ray spectra produced in an anisotropic Inverse Compton (IC) $e^\pm$ pair cascade in the whole volume above the accretion disk. The cascade $γ$-ray spectra are obtained for different locations of the observer in respect to the direction of the jet. We also study the time evolution of this $γ$-ray emission caused by the propagation of the relativistic leptons along the jet and the delays resulting from different places of the origin of $γ$-rays above the accretion disk. We discuss the main features of such a cascade model assuming constant injection rate of electrons along the jet. We are investigating two models for their different maximum energies: constant value independent on the distance along the jet or limited by the synchrotron energy losses considered locally in the jet. The model is discussed in the context of blazars observed at small and large inclination angles taking as an example the parameters of the two famous sources Cen A and 3C 279.